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Answer:
Option C) We would reject the claim that the trains run late an average of 5 minutes and conclude that they run late an average of more than 5 minutes since the 99% confidence interval exceeds 5.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 5 minutes
Sample mean, = 9.130 minutes
Sample size, n = 10
Alpha, α = 0.01
Sample standard deviation, s = 1.4 minutes
First, we design the null and the alternate hypothesis
We have to construct 99% confidence interval.
99% Confidence interval:
Putting the values, we get,
99% Confidence interval: (7.6917,10.5683)
Since the population mean does not lie in he calculated confidence interval, thus, we fail to accept the null hypothesis and accept the alternate hypothesis.
Option C) We would reject the claim that the trains run late an average of 5 minutes and conclude that they run late an average of more than 5 minutes since the 99% confidence interval exceeds 5.